Finite differences for hyperbolic equations

Abstract

In this chapter, we will deal with time-dependent problems of hyperbolic type. For their derivation and for an in-depth analysis see e.g. [Sal08], Chap. 4. We will limit ourselves to considering the numerical approximation using the finite difference method, which was historically the first one to be applied to this type of equations. To introduce in a simple way the basic concepts of the theory, most of our presentation will concern problems depending on a single space variable. Finite element approximations will be addressed in Chap. 13, the extension to nonlinear problems in Chap. 14.